Spectral multidomain technique with Local Fourier Basis II: Decomposition into cells

The spectral multidomain method for the solution of 2-D elliptic and parabolic PDE's is developed. The computational region is decomposed into rectangular cells. A Local Fourier Basis technique is implemented for the discretization in space. Such a technique enables the global (typically ∼10⁴-10⁵) matching relations for the interface unknows to be decoupled into a set of relations for only few interface points at a time.